One of the most fundamental equations in engineering mathematics is Laplace's Equation. A number of physical phenomena are described by this partial differential equation including steady-state heat conduction, incompressible fluid flow, elastostatics, as well as gravitational and electromagnetic fields. The theory of solutions of this equation is called potential theory.
One example of potential theory is electromagnetic field theory, which can be used to distribute objects on a spherical surface. Electromagnetic field theory has been studied extensively over the years for a variety of applications. It has been used, for example, in satellite mirror design. Electromagnetic field theory, including the obvious applications to semiconductor research and computer technology, has many applications in the physical sciences, not limited to celestial mechanics, organic chemistry, geophysics, and structural acoustics.
In many applications, the objects are treated as point charges so that principles of electromagnetic field theory can be applied to determine optimal positioning or to predict the equilibrium positions of the objects.
While the task of distributing point charges on a spherical surface has been studied extensively in mathematical circles, it has not been employed as a tool to develop and define dimple patterns or optimal dimple distributions on a golf ball.
Instead, current golf ball dimple patterns generally are based upon dividing the spherical surface of the ball into discrete polygonal surfaces. The edges of the surfaces join to form geometric shapes that approximate the spherical surface of a golf ball. These geometric shapes include, for example, regular octahedral, regular icosahedral and regular polyhedral arrangements. Once a geometric shape is selected, the polyhedral surfaces are individually filled with a dimple pattern that may be repeated over the surface.
While this approach may be effective in enabling easy dimple design and mold manufacture, it may not result in optimal dimple positioning or distribution for improved aerodynamic performance. In addition, this approach to designing a dimple pattern may result in a golf ball having variations in flight performance depending upon the direction of rotation of the ball. For instance, rotation about one axis may result in different flight characteristics than rotation about a second axis. Moreover, the difference may be large enough to produce a measurable and visible difference in aerodynamic lift and drag.
The potential limitations described above may be present in other methods for arranging dimples on a golf ball. Thus, it would be desirable to have a way to optimize a dimple pattern by repositioning the dimples to improve flight performance.